含参量非正常积分一致收敛性的几个判别方法

Several Criterions about the Convergence of Parameter Improper Integration

含参量非正常积分是研究和表达函数特别是非初等函数的有力工具。通过对比函数项级数一致收敛性的几个判别法(文献[2]),利用函数项级数一致收敛与含参量非正常积分一致收敛间的关系(引理1,定理6),给出了与函数项级数一致收敛性判别法类似的含参量非正常积分一致收敛性判别法,即比式判别法、根式判别法,同时还给出了含参量非正常积分一致收敛性的对数判别法。

The convergence of parameter improper integral is to study and expression in particular non-primary function of a powerful tool.In this thesis,several criterions about the uniform convergence of the function of the series are contrasted,the relationship between（Lemma1,theorem 6） the uniform convergence of the function series and uniform convergence of the parameter improper integration is used,the judging method about the uniform convergence of the parameter improper integration is give which is similar with the criterions about the uniform convergence of the function series.Such as ratio test,radical test,also presented with logarithm test of the uniform convergence of the parameter improper integration.